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u
es,
th
e
h
y
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ter
esi
s
cu
r
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en
t
co
n
tr
o
l
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as
g
o
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m
u
c
h
atte
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u
e
to
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ev
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al
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c
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as
t
h
e
s
i
m
p
licit
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f
its
i
m
p
le
m
en
ta
tio
n
,
it
s
i
n
d
ep
en
d
en
ce
to
c
h
an
g
es
in
p
ar
a
m
ete
r
s
o
f
lo
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p
o
w
er
s
u
p
p
l
y
a
n
d
ab
ilit
y
o
n
c
u
r
r
en
t
li
m
it
in
g
an
d
f
ast c
u
r
r
en
t c
o
n
tr
o
l r
esp
o
n
s
e
[
1
1
].
H
y
s
ter
e
s
is
c
u
r
r
en
t
co
n
tr
o
ller
is
o
n
e
o
f
t
h
e
m
o
s
t
i
m
p
o
r
tan
t
P
W
M
s
w
itc
h
i
n
g
m
e
th
o
d
s
to
p
r
o
d
u
ce
r
ef
er
en
ce
c
u
r
r
en
t
s
[
1
2
]
.
On
th
e
o
th
er
h
a
n
d
co
n
v
e
n
tio
n
al
h
y
s
ter
esis
m
et
h
o
d
in
cl
u
d
es
s
o
m
e
u
n
d
e
s
ir
ab
le
r
esu
l
ts
,
s
u
c
h
a
s
v
ar
iab
le
s
w
i
tch
in
g
f
r
eq
u
en
c
y
t
h
at
ca
u
s
es
a
u
d
io
n
o
is
es,
h
i
g
h
s
w
i
tch
in
g
lo
s
s
es
a
n
d
in
j
ec
tio
n
o
f
h
ig
h
f
r
eq
u
en
c
y
c
u
r
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en
t
co
m
p
o
n
e
n
t
s
to
th
e
s
o
u
r
ce
cu
r
r
e
n
t
t
h
at
m
a
k
es
it
d
i
f
f
icu
lt
to
d
esig
n
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u
itab
le
f
ilter
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to
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e
m
o
v
e
th
ese
h
i
g
h
f
r
eq
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e
n
c
y
h
ar
m
o
n
i
cs.
I
n
[
1
2
]
[
1
3
]
a
p
p
lied
th
e
f
ix
ed
an
d
ad
ap
tiv
e
h
y
s
ter
e
s
is
c
u
r
r
en
t
co
n
tr
o
ller
s
i
n
ac
tiv
e
p
o
w
er
f
ilter
s
.
I
n
[
1
4
]
i
m
p
le
m
e
n
ted
th
e
h
y
s
ter
esi
s
cu
r
r
en
t
co
n
tr
o
l
tech
n
iq
u
e
to
eli
m
in
ate
th
e
h
ar
m
o
n
ic
s
an
d
h
e
n
ce
i
m
p
r
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v
ed
t
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p
o
w
e
r
q
u
alit
y
o
f
m
icr
o
g
r
id
s
y
s
te
m
.
I
n
[
1
5
]
a
P
V
in
v
er
ter
w
it
h
P
I
cu
r
r
en
t
co
n
tr
o
ller
is
u
s
ed
to
m
ai
n
tai
n
co
n
s
ta
n
t
v
o
ltag
e
an
d
to
r
ed
u
ce
h
ar
m
o
n
ics
.
[
1
6
]
s
h
o
w
s
t
h
e
r
esu
lt
s
o
f
th
e
P
V,
FC
b
ased
g
r
id
co
n
n
ec
ted
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y
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te
m
w
it
h
P
I
,
r
am
p
ti
m
e
cu
r
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en
t
co
n
tr
o
l
ler
m
eth
o
d
s
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I
d
en
ti
f
ied
th
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i
x
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b
an
d
h
y
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ter
esi
s
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r
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co
n
tr
o
l
tech
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iq
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e
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o
t
ap
p
lied
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ar
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ee
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m
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r
p
ar
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ec
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f
cu
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en
ts
o
f
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in
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et
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i
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m
ized
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h
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ap
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ev
alu
ates
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o
r
m
an
ce
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h
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h
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o
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r
cu
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co
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tr
o
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o
t
r
eq
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ir
e
th
e
in
f
o
r
m
atio
n
ab
o
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t
th
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ad
an
d
g
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g
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d
d
y
n
a
m
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r
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n
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id
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I
n
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5
to
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%
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th
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s
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m
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r
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Fig
u
r
e
1
s
h
o
w
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t
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v
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all
cir
cu
it d
iag
r
a
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esig
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Fig
u
r
e
1
.
Ov
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2.
F
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AND
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RR
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ase
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W
h
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n
ev
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C
u
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v
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to
r
‘
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w
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h
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esp
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e
f
o
llo
w
i
n
g
[
1
7
]
.
1
)
T
h
e
cu
r
r
en
t
d
if
f
er
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ce
‘
I
e’
s
h
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ld
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y
s
ter
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b
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d
as
s
lo
w
l
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as
p
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s
s
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le
to
ac
h
iev
e
lo
w
s
w
i
tch
in
g
f
r
eq
u
e
n
c
y
.
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I
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Fig
u
r
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2
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T
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Fig
u
r
e
3
.
L
o
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r
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tatio
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Fro
m
eq
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(
1
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th
e
c
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r
en
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er
r
o
r
d
ev
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n
is
dt
d
I
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e
f
dt
dI
dt
d
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(
4
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dt
d
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V
L
dt
d
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DC
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(
5
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Ass
u
m
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dt
d
I
r
e
f
L
e
V
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e
f
(
6
)
V
r
e
f
V
L
dt
d
I
e
DC
1
(
7
)
R
ef
er
e
n
ce
[
18
]
ex
p
lai
n
s
w
h
y
t
h
e
d
ec
is
i
v
e
v
o
lta
g
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f
o
r
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c
u
r
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en
t
co
n
tr
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l
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s
s
u
m
o
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th
e
in
n
er
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an
d
v
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lta
g
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ac
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o
s
s
t
h
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d
u
ct
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o
f
lo
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.
Fro
m
f
ig
u
r
e
.
1
t
h
e
c
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en
t
w
a
v
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f
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as
b
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t
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Fig
u
r
e
4
.
eq
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n
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t
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f
in
v
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ter
w
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e
n
th
e
s
w
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h
es a
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e
tu
r
n
ed
-
on
Fig
u
r
e
5
.
eq
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n
t
cir
cu
i
t
o
f
in
v
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ter
w
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th
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s
w
itc
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es a
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r
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o
f
f
Fo
r
f
ig
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r
e
4
th
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lo
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p
eq
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n
ca
n
b
e
w
r
itte
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as
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I
J
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C
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I
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N:
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0
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r
F
ig
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ass
u
m
p
tio
n
is
m
ad
e
th
at
r
ef
er
en
ce
cu
r
r
en
t
ch
an
g
es l
in
ea
r
l
y
o
v
er
o
n
e
s
w
i
t
ch
in
g
c
y
cle.
2
.
1
T
urn o
f
f
cr
it
er
ia
A
t
t
1
,
th
e
i
n
d
u
c
to
r
cu
r
r
en
t a
n
d
th
e
r
ef
er
en
ce
c
u
r
r
en
t c
an
b
e
ex
p
r
ess
ed
as
0
,
1
)
(
t
I
t
dt
dI
t
I
on
on
(
1
2
)
I
*
is
th
e
r
ef
er
en
ce
c
u
r
r
en
t.
0
,
1
*
t
I
t
dt
dI
t
I
on
(
1
3
)
Fro
m
eq
u
atio
n
s
(
1
2
)
&
(
1
3
)
0
0
,
1
1
t
I
t
I
dt
dI
dt
dI
t
t
I
t
I
on
on
(
1
4
)
I
n
F
ig
u
r
e
.
2
at
t
0
,
0
0
t
I
t
I
I
n
th
e
p
o
s
i
tiv
e
s
ec
t
io
n
(
t
0
-
t
2
)
,
th
e
i
n
s
ta
n
ta
n
eo
u
s
s
lo
p
e
o
f
I
*
is
g
iv
e
n
b
y
on
on
t
t
I
t
I
dt
dI
dt
dI
,
1
1
(1
5
)
A
t
t
2
,
t
h
e
in
d
u
cto
r
cu
r
r
en
t a
n
d
r
ef
er
en
ce
cu
r
r
en
t
ar
e
ex
p
r
ess
ed
as
1
,
2
t
I
t
dt
dI
t
I
o
f
f
o
f
f
(1
6
)
1
,
2
t
I
t
dt
dI
t
I
of
f
(1
7
)
Fro
m
eq
u
atio
n
s
(
1
6
)
&
(
1
7
)
2
2
,
1
1
t
I
t
I
dt
dI
dt
dI
t
t
I
t
I
o
f
f
o
f
f
(1
8
)
I
n
f
i
g
u
r
e
2
at
t
0
I
*
(t
2
)
=
I
(
t
2
)
dt
dI
dt
dI
t
I
t
I
t
o
f
f
o
f
f
1
1
,
(
1
9
)
B
y
s
o
lv
i
n
g
th
e
eq
u
at
io
n
s
(
1
2
)
to
(
1
5
)
1
,
1
1
,
1
2
on
DC
o
f
f
t
t
I
t
I
L
V
t
(2
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
5
,
Octo
b
er
2
0
1
7
:
2
3
0
0
–
2
3
0
8
2304
T
h
e
tu
r
n
o
f
f
ti
m
e
is
esti
m
ated
u
s
i
n
g
th
e
eq
u
atio
n
(
2
0
)
w
it
h
in
s
ta
n
ta
n
eo
u
s
f
ee
d
b
ac
k
s
i
g
n
al
s
.
T
h
e
tu
r
n
-
o
f
f
cr
iter
io
n
is
t
h
e
ti
m
e
o
f
I
–
I
*
in
p
o
s
itiv
e
c
y
cle
t
h
at
i
s
eq
u
al
to
h
a
lf
t
h
e
s
w
itc
h
in
g
c
y
cle
as
s
h
o
w
n
i
n
F
ig
u
r
e
2
.
2
,
,
T
t
t
on
o
f
f
an
d
0
I
I
(2
1
)
W
h
er
e
‘
T
’
is
th
e
s
w
itc
h
in
g
p
e
r
io
d
.
B
ased
o
n
eq
u
atio
n
s
(
1
9
)
an
d
(2
0
)
,
th
e
co
n
tr
o
ller
ca
n
d
eter
m
in
e
th
e
t
u
r
n
-
o
f
f
ac
t
io
n
at
t
h
e
m
o
s
t su
i
tab
le
ti
m
e.
2
.
2
T
urn
–
O
n Cr
it
er
ia
:
I
n
th
e
n
eg
at
iv
e
s
ec
tio
n
(
t
2
-
t
4
)
,
th
e
in
s
ta
n
tan
eo
u
s
s
lo
p
e
I
*
is
g
i
v
en
b
y
o
f
f
o
f
f
t
t
I
t
I
dt
dI
dt
dI
,
3
3
*
(2
2
)
B
ased
o
n
th
e
s
lo
p
e
t
-
,
on
is
p
r
ed
icted
as
dt
dI
dt
dI
t
I
t
I
t
on
on
3
3
,
(2
3
)
B
y
u
s
i
n
g
eq
u
atio
n
s
(
1
1
)
&
(
1
2
)
1
,
3
3
,
]
1
2
[
o
f
f
DC
on
t
t
I
t
I
L
V
t
(
2
4
)
Fro
m
eq
u
atio
n
(
2
5
)
th
e
t
u
r
n
-
o
n
ti
m
e
is
e
s
ti
m
ated
w
it
h
i
n
s
tan
ta
n
eo
u
s
f
ee
d
b
ac
k
s
i
g
n
als.
T
h
e
tu
r
n
o
n
cr
iter
ia
is
th
e
ti
m
e
o
f
I
-
I
*
i
n
n
eg
ati
v
e
c
y
cle
a
n
d
is
eq
u
al
to
h
alf
s
w
i
tc
h
i
n
g
c
y
cle
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
2
.
T
h
u
s
:
2
,
,
T
t
t
on
o
f
f
an
d
0
I
I
(2
5
)
B
ased
o
n
eq
u
atio
n
s
(
2
4
)
&
(
2
5
)
th
e
co
n
tr
o
ller
ca
n
b
e
d
esi
g
n
ed
.
T
h
e
s
w
itc
h
i
n
g
f
u
n
ctio
n
f
o
r
p
h
ase
A
i
s
d
er
iv
ed
f
r
o
m
t
h
e
ab
o
v
e
t
u
r
n
-
o
n
an
d
t
u
r
n
-
o
f
f
cr
iter
ia,
f
o
r
o
th
er
t
w
o
p
h
ase
s
B
an
d
C
r
ef
er
en
ce
cu
r
r
en
t
s
f
o
r
th
o
s
e
p
h
a
s
es h
a
s
to
co
n
s
id
er
t
o
s
o
lv
e
th
e
s
w
itch
in
g
f
u
n
ctio
n
.
3.
I
NS
T
AN
T
ANEOU
S P
-
Q
P
O
WE
R
T
H
E
O
RY
T
h
e
r
eg
u
lar
r
ef
er
en
ce
c
u
r
r
en
t
ev
o
ca
tio
n
t
h
eo
r
y
is
t
h
e
i
n
s
ta
n
t
an
eo
u
s
p
-
q
p
o
w
er
th
eo
r
y
in
t
h
r
ee
p
h
ase
cir
cu
its
.
R
ea
l
an
d
r
ea
cti
v
e
p
o
w
er
t
h
eo
r
y
co
n
s
id
er
s
th
e
t
h
r
e
e
p
h
ase
s
y
s
te
m
as
a
u
n
it
n
o
t
a
s
a
s
u
p
er
p
o
s
itio
n
o
r
s
u
m
o
f
t
h
r
ee
s
in
g
le
p
h
ase
cir
cu
its
.
C
lar
k
’
s
tr
an
s
f
o
r
m
atio
n
tech
n
iq
u
e
is
u
s
ed
to
co
n
v
er
t
th
r
ee
p
h
ase
v
o
lta
g
e
s
an
d
cu
r
r
en
t
s
f
r
o
m
a
-
b
-
c
co
-
o
r
d
in
ates to
α
-
β
-
0
co
-
o
r
d
in
ates.
I
n
o
th
er
w
o
r
d
s
t
h
i
s
C
lar
k
s
tr
an
s
f
o
r
m
atio
n
co
n
v
er
t
s
n
atu
r
al
t
h
r
ee
p
h
ase
co
o
r
d
in
ate
s
y
s
te
m
i
n
to
a
s
tat
io
n
ar
y
t
w
o
p
h
ase
r
ef
er
e
n
ce
f
r
a
m
e.
Ass
u
m
e
a
th
r
ee
p
h
a
s
e
lo
ad
w
i
th
t
h
e
in
s
ta
n
ta
n
eo
u
s
v
o
lta
g
es
as
v
(
t)
=[
v
a
(
t)
v
b
(
t)
v
c
(
t)
]
t
an
d
th
e
in
s
ta
n
tan
eo
u
s
cu
r
r
en
ts
I
(
t)
=[
I
a
(
t)
I
b
(
t)
I
c
(
t)
]
t
.
B
y
u
s
in
g
C
lar
k
s
tr
a
n
s
f
o
r
m
a
tio
n
:
c
b
a
v
v
v
v
v
v
2
3
2
3
0
2
1
2
1
1
2
1
2
1
2
1
3
2
0
(
2
7
)
c
b
a
I
I
I
I
I
I
2
3
2
3
0
2
1
2
1
1
2
1
2
1
2
1
3
2
0
(
2
8
)
I
I
I
,
,
0
ar
e
th
e
ze
r
o
s
eq
u
en
ce
cu
r
r
en
t,
α
ax
i
s
cu
r
r
en
t,
β a
x
i
s
cu
r
r
en
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
C
u
r
r
en
t Co
n
tr
o
lle
r
B
a
s
ed
P
o
w
er Ma
n
a
g
eme
n
t S
tr
a
teg
y
fo
r
I
n
terf
a
cin
g
DG
Un
its
…
(
N
.
C
h
a
ita
n
ya
)
2305
T
h
is
C
lar
k
s
tr
an
s
f
o
r
m
a
tio
n
is
u
s
ed
to
a
n
al
y
ze
t
h
e
h
ea
lt
h
y
an
d
w
ea
k
p
o
r
tio
n
,
ac
co
r
d
in
g
to
t
h
e
o
u
tp
u
t
P
W
M
p
u
ls
e
is
g
e
n
er
ated
an
d
f
ed
to
th
e
i
n
v
er
ter
s
ec
tio
n
b
e
ca
u
s
e
o
f
th
is
t
h
e
D
C
is
a
g
ai
n
co
n
v
er
ted
to
th
r
ee
p
h
ase
A
C
m
o
r
e
p
u
l
s
e
is
p
r
o
f
u
ce
d
i
n
w
ea
k
p
o
r
tio
n
p
h
ase
an
d
h
en
ce
m
o
r
e
p
o
w
er
is
i
n
j
ec
ted
to
w
ar
d
s
t
h
e
tr
an
s
m
is
s
io
n
li
n
e
s
th
r
o
u
g
h
th
e
tr
an
s
f
o
r
m
er
an
d
h
e
n
ce
p
o
w
er
f
ac
to
r
co
m
p
en
s
atio
n
i
s
o
b
tain
e
d
.
C
o
n
s
id
er
ze
r
o
s
eq
u
en
ce
cu
r
r
en
t is
eq
u
a
l to
ze
r
o
,
th
u
s
i
n
s
ta
n
t
an
eo
u
s
p
&
q
ca
n
b
e
ca
lcu
late
d
as
:
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
t
I
t
I
t
v
t
v
t
v
t
v
t
q
t
p
(
2
9
)
P
(
t)
an
d
q
(
t)
ca
n
b
e
s
ep
ar
ate
i
n
to
av
er
ag
e
p
ar
ts
a
n
d
o
s
cillati
n
g
p
ar
ts
,
f
r
o
m
liter
at
u
r
e
it
is
well
k
n
o
w
n
th
at
t
h
e
av
er
a
g
e
r
ea
l
p
o
w
er
ca
n
p
r
o
d
u
ce
f
r
o
m
f
u
n
d
a
m
e
n
tal
h
ar
m
o
n
ics
o
f
th
e
lo
ad
cu
r
r
en
t
p
o
s
itiv
e
s
eq
u
e
n
ce
co
m
p
o
n
e
n
t
.
A
cc
o
r
d
in
g
l
y
i
n
o
r
d
er
to
co
m
p
en
s
ate
h
ar
m
o
n
ics
an
d
in
s
ta
n
tan
eo
u
s
r
ea
ctiv
e
p
o
w
er
r
e
f
e
r
en
ce
cu
r
r
e
n
ts
ca
n
ex
tr
ac
ted
as
:
)
(
~
)
(
~
)
(
)
(
)
(
)
(
)
(
)
(
1
t
q
t
p
t
v
t
v
t
v
t
v
t
I
t
I
(
3
0
)
t
c
b
a
t
I
t
I
t
I
t
I
t
I
)
(
)
(
0
2
3
2
3
0
2
1
2
1
1
2
1
2
1
2
1
3
2
)
(
)
(
)
(
1
1
(3
1
)
4.
SI
M
UL
AT
I
O
N
R
E
S
UL
T
S
AND
ANA
L
YS
I
S
P
V
ce
ll,
Fu
el
ce
lls
ar
e
t
h
e
t
w
o
DC
v
o
ltag
e
s
o
u
r
ce
s
u
s
ed
as
DG
u
n
it
s
i
n
t
h
is
s
y
s
te
m
,
to
c
h
an
g
e
th
e
s
e
t
w
o
D
G’
s
o
u
tp
u
t
v
o
ltag
e
to
t
h
e
d
esire
d
in
v
er
ter
in
p
u
t
v
o
ltag
e
an
d
s
m
o
o
th
th
e
t
w
o
DG
’
s
o
u
tp
u
t
cu
r
r
en
t
n
ee
d
is
t
h
er
e
to
ad
o
p
t
a
D
C
/D
C
b
o
o
s
t
co
n
v
er
ter
.
E
ac
h
3
5
k
w
r
a
ted
P
V,
Fu
el
ce
lls
ar
e
ad
o
p
ted
f
o
r
t
h
is
s
t
u
d
y
,
th
e
P
V,
Fu
el
ce
ll
o
u
tp
u
t
v
o
lta
g
e
i
s
4
0
0
v
o
lts
,
b
o
o
s
t
u
p
to
7
0
0
v
o
lts
u
s
i
n
g
D
C
/D
C
co
n
v
er
ter
,
Her
e
th
e
co
n
tr
o
ller
f
o
r
th
e
co
n
v
er
ter
is
u
s
ed
to
r
e
g
u
la
te
th
e
DC
b
u
s
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lta
g
e
w
it
h
in
a
d
esira
b
le
r
an
g
e.
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h
e
o
u
tp
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t
v
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lta
g
e
o
f
th
e
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b
o
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s
t
co
n
v
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ter
is
f
e
d
to
DC
/A
C
i
n
v
er
ter
.
T
h
r
o
u
g
h
th
e
p
o
in
t
o
f
co
m
m
o
n
co
u
p
lin
g
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e
in
v
er
ter
is
co
n
n
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ted
to
t
h
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g
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id
,
t
w
o
R
L
lo
ad
s
ar
e
co
n
n
ec
ted
at
t
h
e
p
o
in
t
o
f
co
m
m
o
n
co
u
p
li
n
g
.
T
h
e
in
v
er
ter
is
al
w
a
y
s
m
ai
n
tai
n
s
th
e
o
u
tp
u
t
v
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g
e
a
cc
o
r
d
in
g
to
th
e
r
ef
er
e
n
ce
v
alu
e
an
d
at
t
h
e
s
a
m
e
ti
m
e
in
n
er
c
u
r
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en
t
co
n
tr
o
l
lo
o
p
is
u
s
ed
to
a
v
o
id
th
e
cir
cu
lati
n
g
cu
r
r
en
ts
o
f
b
o
th
th
e
p
ar
allel
i
n
v
er
ter
s
.
Fig
u
r
e
6
s
h
o
w
s
th
e
DC
b
u
s
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e
o
f
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P
V
ce
ll.
Ma
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in
t
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ac
k
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n
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ac
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1
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1
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ee
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g
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r
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7
s
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Fig
u
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s
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es a
n
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o
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er
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le
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2
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3
s
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b
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th
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co
n
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tech
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iq
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s
h
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etter
p
er
f
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ce
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d
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ter
s
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f
f
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it
m
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b
ac
k
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it
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a
s
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t sp
an
o
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h
ase
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ck
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lo
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t u
s
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te
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e
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r
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ac
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r
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Fig
u
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s
h
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c
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t i
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at
0
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2
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c
u
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o
n
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b
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ad
is
in
c
r
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s
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d
u
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ad
d
itio
n
o
f
an
o
t
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er
lo
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w
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th
a
s
li
g
h
t
d
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to
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th
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co
n
s
i
d
er
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tech
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u
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m
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y
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ate
t
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a
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er
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2
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3
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ec
th
e
cu
r
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en
t
s
u
p
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lied
to
t
h
e
lo
ad
is
i
n
cr
ea
s
ed
to
9
0
a
m
p
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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C
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Vo
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5
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2306
Fig
u
r
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DC
b
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el
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Fig
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DC
b
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ll in
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Fig
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.
R
L
C
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,
R
L
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Fig
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r
e
9
.
lo
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cu
r
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t in
a
m
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s
Fig
u
r
e
10
.
h
ar
m
o
n
ic
d
is
to
r
tio
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o
f
lo
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cu
r
r
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t
Fig
u
r
e
1
1
.
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n
v
er
ter
1
o
u
tp
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u
r
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t in
a
m
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Fig
u
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e
12
.
in
v
er
ter
2
o
u
tp
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t c
u
r
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t in
a
m
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s
Fig
u
r
e
13
.
T
HD
o
f
in
v
er
ter
o
u
tp
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t c
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r
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t
Fig
u
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e
1
0
s
h
o
w
s
t
h
e
h
ar
m
o
n
ic
d
is
to
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tio
n
s
o
f
t
h
e
lo
ad
cu
r
r
en
t
f
o
r
th
e
f
ir
s
t
2
0
cy
cle
s
i.e
f
r
o
m
0
s
ec
’
s
to
0
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4
s
ec
’
s
i
s
1
.
3
2
%
w
h
ic
h
is
v
er
y
les
s
v
al
u
e.
F
ig
u
r
e
1
1
an
d
Fig
u
r
e
1
2
s
h
o
w
s
i
n
v
er
ter
1
an
d
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n
v
er
ter
2
o
u
tp
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t
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en
t
in
a
m
p
s
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ec
au
s
e
t
h
e
t
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r
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ar
e
h
a
v
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n
g
t
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e
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a
m
e
ca
p
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it
y
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o
th
e
cu
r
r
en
t
s
u
p
p
lied
b
y
b
o
th
t
h
e
s
o
u
r
ce
s
ar
e
s
a
m
e
a
n
d
b
o
th
i
n
v
er
ter
s
ar
e
co
n
n
ec
ted
in
p
ar
allel
s
o
th
er
e
is
n
o
n
ee
d
o
f
v
o
ltag
e
co
n
tr
o
ller
au
to
m
at
icall
y
f
o
r
th
e
p
ar
allel
co
n
ee
cted
s
y
s
te
m
t
h
e
v
o
lta
g
e
w
ill
b
ec
o
m
e
s
a
m
e.
Fi
g
u
r
e.
1
3
s
h
o
w
s
th
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
o
f
in
v
er
t
er
o
u
tp
u
t
cu
r
r
en
t
f
o
r
th
e
f
ir
s
t
2
0
cy
cles
p
er
io
d
th
e
h
ar
m
o
n
ic
d
is
to
r
tio
n
is
v
er
y
less
i.e
0
.
9
1
%.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
C
u
r
r
en
t Co
n
tr
o
lle
r
B
a
s
ed
P
o
w
er Ma
n
a
g
eme
n
t S
tr
a
teg
y
fo
r
I
n
terf
a
cin
g
DG
Un
its
…
(
N
.
C
h
a
ita
n
ya
)
2307
Fig
u
r
e.
1
4
T
o
tal
cu
r
r
en
t o
f
b
o
th
th
e
i
n
v
er
ter
s
in
a
m
p
s
Fig
u
r
e.
1
5
I
n
v
er
ter
1
o
u
tp
u
t v
o
ltag
e
i
n
v
o
lt
s
Fig
u
r
e.
1
6
I
n
v
er
ter
2
o
u
tp
u
t v
o
ltag
e
i
n
v
o
lt
s
Fig
u
r
e.
1
7
C
u
r
r
en
t s
u
p
p
lied
to
th
e
g
r
id
Fig
u
r
e
1
8
.
T
HD
o
f
cu
r
r
en
t s
u
p
p
lied
to
th
e
g
r
id
Fig
u
r
e
19
.
R
ea
l a
n
d
r
ea
ctiv
e
p
o
w
er
co
n
s
u
m
ed
b
y
lo
ad
Fig
u
r
e
1
4
s
h
o
w
s
t
h
e
o
u
tp
u
t
c
u
r
r
en
t
o
f
b
o
th
t
h
e
in
v
er
ter
s
i
n
a
m
p
s
.
F
ig
u
r
e
1
5
an
d
F
ig
u
r
e
1
6
s
h
o
w
t
h
e
o
u
tp
u
t
v
o
lta
g
e
o
f
b
o
th
th
e
i
n
v
er
ter
s
in
v
o
lts
.
Fi
g
u
r
e
1
7
s
h
o
w
s
t
h
e
cu
r
r
e
n
t
s
u
p
p
lied
to
th
e
g
r
id
in
a
m
p
s
to
test
th
e
s
tab
ilit
y
a
n
d
tr
ac
k
i
n
g
ca
p
a
b
ilit
y
o
f
th
e
co
n
s
id
er
ed
co
n
tr
o
ller
th
e
lo
ad
is
in
cr
ea
s
ed
f
r
o
m
0
.
2
s
ec
s
to
0
.
3
s
ec
d
u
r
i
n
g
th
at
ti
m
e
t
h
e
cu
r
r
en
t
s
u
p
p
lied
to
th
e
g
r
id
is
r
ed
u
ce
d
in
s
ta
n
tl
y
.
Fi
g
u
r
e
1
8
s
h
o
w
s
t
h
e
T
HD
o
f
cu
r
r
en
t
s
u
p
p
lied
to
t
h
e
g
r
id
f
o
r
th
e
f
ir
s
t
1
5
c
y
c
les
i
s
0
.
3
4
%
.
Fi
g
u
r
e
1
9
s
h
o
w
s
th
e
r
ea
l
a
n
d
r
ea
ctiv
e
p
o
w
er
s
co
n
s
u
m
ed
b
y
t
h
e
lo
ad
.
5.
CO
NCLU
SI
O
N
Fro
m
liter
at
u
r
e
it
is
o
b
s
er
v
ed
th
er
e
i
s
a
s
co
p
e
to
ap
p
l
y
b
o
th
l
in
ea
r
a
n
d
n
o
n
li
n
ea
r
c
u
r
r
en
t
co
n
tr
o
l
m
et
h
o
d
s
f
o
r
p
ar
allel
co
n
n
ec
t
ed
DG
b
ased
in
v
er
ter
s
.
T
h
is
p
ap
er
ev
alu
ates
th
e
p
er
f
o
r
m
an
ce
o
f
n
o
n
li
n
ea
r
cu
r
r
en
t
co
n
tr
o
l
m
et
h
o
d
i.e
f
ix
ed
b
an
d
h
y
s
ter
e
s
is
cu
r
r
e
n
t
co
n
tr
o
l
m
et
h
o
d
w
it
h
o
u
t
P
L
L
f
o
r
th
e
p
ar
allel
co
n
n
ec
ted
DG
b
ased
s
y
s
te
m
.
T
h
e
co
n
clu
s
io
n
s
t
h
at
ca
n
b
e
d
r
a
w
n
f
r
o
m
th
i
s
p
ap
er
ar
e:
1
.
A
n
o
v
el
P
V
,
FC
b
ased
p
ar
allel
co
n
n
ec
ted
s
y
s
te
m
i
n
ter
f
ac
ed
to
g
r
id
is
p
r
o
p
o
s
ed
.
2
.
Fix
ed
b
an
d
h
y
s
ter
e
s
is
c
u
r
r
en
t
co
n
tr
o
l
w
it
h
P
Q
p
o
w
er
th
eo
r
y
is
p
r
o
p
o
s
ed
f
o
r
th
e
p
ar
allel
co
n
n
ce
td
s
y
s
te
m
s
.
3.
T
o
test
th
e
s
tab
ilit
y
a
n
d
tr
ac
k
in
g
ca
p
ab
ilit
y
w
h
i
le
d
eter
m
i
n
in
g
th
e
r
ef
er
en
ce
cu
r
r
e
n
t
a
v
ar
iab
le
lo
ad
co
n
d
itio
n
is
ap
p
lied
an
d
o
b
s
er
v
ed
th
e
r
es
u
lts
.
4
.
Du
e
to
th
e
i
n
co
r
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Evaluation Warning : The document was created with Spire.PDF for Python.
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RE
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NC
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[1
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In
tern
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rg
y
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c
y
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Eu
ro
p
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o
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lf
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p
p
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[3
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Blaa
b
jerg
F
,
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e
C,
Kia
e
r
S
B.
P
o
w
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r
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lec
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terfa
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T
ra
n
sa
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ti
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r ele
c
tro
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ic
s.
2
0
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):
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84
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.
[4
]
OJ
P
e
ti
n
rin
,
M
S
h
a
a
b
a
n
,
"
Ov
e
rc
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rid
,
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m
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o
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1
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n
o
.
2
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p
p
.
2
2
9
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3
4
,
2
0
1
2
.
[5
]
JP
P
i
n
t
o
,
R
P
re
g
it
z
e
r,
L
F
C
M
o
n
teiro
a
n
d
JL
Af
o
n
so
n
.
3
-
P
h
a
se
4
wire
sh
u
n
t
a
c
ti
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e
p
o
we
r
fi
lt
e
r
wit
h
re
n
e
wa
b
le
e
n
e
rg
y
in
ter
fa
c
e
.
IEE
E
Co
n
f
.
o
n
Re
n
e
wa
b
le
En
e
rg
y
&
P
o
w
e
r
Qu
a
li
ty
.
S
e
v
il
le,
S
p
a
in
,
2
0
0
7
.
[6
]
S
Bu
so
a
n
d
P
M
a
tt
a
v
e
ll
i
.
Dig
it
a
l
Co
n
tr
o
l
i
n
P
o
w
e
r
El
e
c
tro
n
ics
.
M
o
rg
a
n
&
Cla
y
p
o
o
l.
2
0
0
6
;
1
.
[7
]
L
M
a
les
a
n
i,
P
M
a
tt
a
v
e
ll
i
a
n
d
P
T
o
m
a
sin
.
Hig
h
-
p
e
rf
o
r
m
a
n
c
e
h
y
ste
re
sis
m
o
d
u
latio
n
tec
h
n
i
q
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e
f
o
r
a
c
ti
v
e
f
il
ters
.
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r E
le
c
tro
n
ics
.
1
9
9
7
;
1
2
:
8
7
6
-
8
8
4
.
[8
]
CT
P
a
n
,
YS
Hu
a
n
g
a
n
d
TL
Jo
n
g
.
A
c
o
n
sta
n
t
h
y
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a
n
d
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t
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ll
e
r
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h
fi
x
e
d
switch
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g
fre
q
u
e
n
c
y
.
IEE
E
In
tern
a
ti
o
n
a
l
sy
m
p
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siu
m
o
n
In
d
u
strial
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e
c
tro
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ics
.
IS
I
E
2
0
0
2
,
3
:
1
0
2
1
-
1
0
2
4
.
[9
]
AW
Krie
g
a
r
a
n
d
JC
S
a
l
m
o
n
.
Hy
ste
re
sis
b
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se
d
c
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rr
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t
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o
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t
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q
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e
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n
y
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wit
h
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re
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n
a
ti
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g
in
teg
r
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to
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t
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li
min
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te t
h
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ste
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d
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te
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r
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n
a
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tri
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ter en
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e
rin
g
.
2
0
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5
:
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1
2
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5
1
6
.
[1
0
]
J
Ro
d
rig
u
e
z
,
J
P
o
n
tt
,
CA
S
il
v
a
,
P
C
o
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a
,
P
L
e
z
a
n
a
,
P
C
o
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n
d
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A
m
m
a
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n
.
p
re
d
ictiv
e
c
u
rr
e
n
t
c
o
n
tro
l
o
f
a
v
o
lt
a
g
e
so
u
rc
e
in
v
e
rter.
IEE
E
T
r
a
n
sa
c
ti
o
n
s o
n
i
n
d
u
stria
l
e
lec
tro
n
ic
s
.
2
0
0
7
;
5
4
:
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9
5
-
50
3.
[1
1
]
A
Bo
u
a
f
ia,
F
Kri
m
.
A
f
u
z
z
y
lo
g
ic
b
a
se
d
c
o
n
tro
l
ler f
o
r
th
re
e
p
h
a
se
P
W
M
re
c
ti
f
ier
w
it
h
u
n
it
y
p
o
w
e
r
fa
c
to
r
o
p
e
ra
ti
o
n
.
ES
R
Gr
o
u
p
s,
J
o
u
r
n
a
l
o
f
El
e
c
ric
a
l
S
y
ste
ms
.
2
0
0
8
;
4
(
1
):
36
-
50.
[1
2
]
Ha
n
i
V
a
h
e
d
i,
A
b
d
o
lrez
a
S
h
e
ik
h
o
les
lam
i,
M
o
h
a
m
m
a
d
T
a
v
a
k
o
l
i
Bin
a
a
n
d
M
a
h
m
o
o
d
V
a
h
e
d
i
.
Re
v
ie
w
a
n
d
S
im
u
latio
n
o
f
F
ix
e
d
a
n
d
A
d
a
p
ti
v
e
Hy
ste
re
sis
Cu
rre
n
t
Co
n
tr
o
l
C
o
n
sid
e
rin
g
S
w
it
c
h
in
g
L
o
ss
e
s
a
n
d
Hig
h
F
re
q
u
e
n
c
y
Ha
r
m
o
n
ics
.
Ad
v
a
n
c
e
s in
p
o
we
r e
lec
tro
n
ics
.
2
0
1
1
;
1
1
:
1
-
6.
[1
3
]
S
e
y
e
d
M
e
h
d
i
A
b
e
d
i
a
n
d
Ha
n
i
V
a
h
e
d
ib
.
S
im
p
li
f
ied
Ca
lcu
latio
n
o
f
A
d
a
p
ti
v
e
H
y
ste
re
sis
c
u
rre
n
t
c
o
n
tr
o
l
to
b
e
u
se
d
i
n
a
c
ti
v
e
p
o
w
e
r
f
il
ter.
T
re
n
d
s in
Ap
p
li
e
d
S
c
ien
c
e
s R
e
se
a
rc
h
.
2
0
1
3
;
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(
1
):
46
-
5
4
.
[1
4
]
M
T
a
m
il
S
e
lv
i,
D
G
u
n
a
p
riy
a
.
A
p
o
w
e
r
q
u
a
li
ty
im
p
ro
v
e
m
n
e
t
f
o
r
m
i
c
ro
g
rid
in
v
e
rter
o
p
e
ra
ted
i
n
g
rid
c
o
n
n
e
c
ted
a
n
d
g
rid
d
isc
o
n
n
e
c
ted
m
o
d
e
s.
Bu
ll
e
ti
n
o
f
El
e
c
trica
l
En
g
i
n
e
e
rin
g
a
n
d
In
f
o
rm
a
ti
c
s
.
2
0
1
4
;
3
(2
)
:
1
1
3
-
1
1
8
.
[1
5
]
DV
N
A
n
a
n
th
,
G
V
Na
g
e
sh
Ku
m
a
r.
De
sig
n
o
f
so
lar
P
V
c
e
ll
b
a
se
d
in
v
e
rter
f
o
r
u
n
b
a
lan
c
e
d
a
n
d
d
ist
o
rted
in
d
u
stria
l
lo
a
d
s.
I
n
d
o
n
e
sia
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
i
n
e
e
rin
g
A
n
d
In
f
o
rm
a
ti
c
s
.
2
0
1
5
;
3
(2
)
:
7
0
-
7
7
.
[1
6
]
N
Ch
a
it
a
n
y
a
,
Dr
K
Ch
a
n
d
ra
S
e
k
h
a
r,
Dr
K
S
R
A
n
jan
e
y
u
lu
.
C
u
rre
n
t
c
o
n
tr
o
ll
e
r
b
a
se
d
p
o
w
e
r
m
a
n
a
g
e
m
e
n
t
stra
teg
y
o
f
g
rid
c
o
n
n
e
c
ted
p
a
ra
ll
e
l
i
n
v
e
rters
fo
r
d
istr
ib
u
ted
g
e
n
e
ra
ti
o
n
a
p
p
li
c
a
ti
o
n
s.
A
u
t
o
ma
ti
c
c
o
n
tro
l
a
n
d
sy
ste
m
e
n
g
in
e
e
rin
g
.
2
0
1
6
;
1
6
(
1
):
38
-
44
.
[1
7
]
Bo
u
z
id
A
ll
a
l,
G
u
e
rre
ro
Jo
se
p
M
,
Ch
e
rit
i
A
h
m
e
d
,
Bo
u
h
a
m
id
a
M
o
h
a
m
e
d
,
S
ica
rd
P
ierre
,
Be
n
g
h
a
n
e
m
M
u
sta
p
h
a
.
A
S
u
rv
e
y
o
n
Co
n
tro
l
o
f
El
e
c
tri
c
P
o
w
e
r
Distrib
u
ted
G
e
n
e
ra
ti
o
n
S
y
s
tem
s
f
o
r
M
icro
g
rid
A
p
p
li
c
a
ti
o
n
s.
Ren
e
wa
b
le
&
S
u
sta
in
a
b
le E
n
e
rg
y
Rev
iews
.
2
0
1
5
:
1
-
2
5
.
[1
8
]
A
Ac
k
v
a
,
H Re
in
o
ld
,
R
Ole
sin
sk
i
.
A
si
m
p
le
a
n
d
se
l
f
a
d
a
p
ti
n
g
h
ig
h
p
e
rf
o
r
m
a
n
c
e
c
u
rre
n
t
sc
h
e
m
e
fo
r
th
re
e
p
h
a
se
v
o
lt
a
g
e
so
u
rc
e
in
v
e
rter.
PE
CS
T
o
l
e
d
o
1
9
9
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.